Question

In a random sample of 20 NBA basketball games the mean number of points scored by the home team was 100.4 with a standard deviation of 4.86.

Create and interpret a 95% confidence interval for the true mean number of points scored by an NBA basketball team at home.
You and your friend were watching a LA Lakers game where they were not playing at home. They only scored 98 points. Your friend says, "Wow, I bet if they were playing at home they would have scored a lot more points." Do you agree or disagree with your friend? Support your detailed answer.

Answer 1

The 95% confidence interval is
`98.27 < \mu < 102.53`

This interval means that there 95% confidence that the true mean is within this interval

Yes i would agree with my friend because the lower and the upper limit 95% confidence interval for mean points scored at home is greater than 98 points

Explanation:

From the question we are told that

The sample size is n = 20

The sample mean is
`\mu = 100.4`

The standard deviation is
`\sigma = 4.86`

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

`\alpha = 100 - 95`

`\alpha = 5\%`

`\alpha = 0.05`

Next we obtain the critical value of
`( \alpha )/(2)` from the normal distribution table, the value is

`Z_{( \alpha )/(2) } = 1.96`

Generally the margin of error is mathematically represented as

`E = Z_{(\alpha )/(2) } * (\sigma)/( √(n) )`

substituting values

`E = 1.96 * ( 4.86 )/( √(20 ) )`

`E = 2.13`

The 95% confidence interval is mathematically represented as

`\= x - E < \mu < \= x + E`

substituting values

`100.4 - 2.13 < \mu < 100.4 + 2.13`

`98.27 < \mu < 102.53`